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A324426 a(n) = Product_{i=1..n, j=1..n} (i^3 + j^3). 14

%I #28 Dec 08 2023 04:51:15

%S 1,2,2592,134425267200,3120795915109442519040000,

%T 180825857777547616919759624941086965760000000,

%U 99356698720512072045648926659510730227553351200000695922065408000000000

%N a(n) = Product_{i=1..n, j=1..n} (i^3 + j^3).

%F a(n) ~ A * 2^(2*n*(n+1) + 1/4) * exp(Pi*(n*(n+1) + 1/6)/sqrt(3) - 9*n^2/2 - 1/12) * n^(3*n^2 - 3/4) / (3^(5/6) * Pi^(1/6) * Gamma(2/3)^2), where A is the Glaisher-Kinkelin constant A074962.

%F a(n) = A079478(n) * A367543(n). - _Vaclav Kotesovec_, Nov 22 2023

%F For n>0, a(n)/a(n-1) = A272246(n)^2 / (2*n^9). - _Vaclav Kotesovec_, Dec 02 2023

%p a:= n-> mul(mul(i^3+j^3, i=1..n), j=1..n):

%p seq(a(n), n=0..7); # _Alois P. Heinz_, Jun 24 2023

%t Table[Product[i^3+j^3, {i, 1, n}, {j, 1, n}], {n, 1, 10}]

%o (PARI) a(n) = prod(i=1, n, prod(j=1, n, i^3+j^3)); \\ _Michel Marcus_, Feb 27 2019

%o (Python)

%o from math import prod, factorial

%o def A324426(n): return prod(i**3+j**3 for i in range(1,n) for j in range(i+1,n+1))**2*factorial(n)**3<<n # _Chai Wah Wu_, Nov 26 2023

%Y Cf. A079478, A324403, A324437, A324438, A324439, A324440, A367834.

%Y Cf. A272246, A307210, A367517, A367543.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 27 2019

%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)